Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x - 3$ and $ BC = 3x + 12$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x - 3} = {3x + 12}$ Solve for $x$ $ 3x = 15$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({5}) - 3$ $ BC = 3({5}) + 12$ $ AB = 30 - 3$ $ BC = 15 + 12$ $ AB = 27$ $ BC = 27$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {27} + {27}$ $ AC = 54$